Question 0121

A function ${f}$ is defined by ${f(x)=ax^3+bx^2+cx+d.}$ The graph of ${y=f(x)}$ passes through the points ${(-1, 13)}$ and ${(1, - 15).}$ The graph has a turning point at ${x=-1,}$ and ${\displaystyle \int_0^1 f(x) \; \mathrm{d}x = - 7.}$